Is a film actor a "thespian"?
Solution 1:
It’s predominantly, but not exclusively, used for stage actors.
Dictionaries — Merriam Webster and the OED — define it just as actor, without restriction. Searching well-edited English-language newspapers and browsing through the top hits confirms, though, that it is associated much more with stage than screen: New York Times, The Guardian, Sydney Morning Herald.
(Ideally, a COCA or Ngrams search would be better, as @msh210 suggests in comments, but I haven’t managed to think of a query that would work well for this question.)
Solution 2:
Originally it was Thespian (from Thespis the legendary founder of theatre in Athens), and referred only to study of tragedy and by extension the theatre in general. (My Chambers dictionary has "an actor (jocular)", so would presumably be horrified to think it might be extended to a performer in the kinematographs). But words change, and I would think a word for 'someone who performs in the theatre only' would be so little used as to be useless. My own feeling is that thespian has a flavour of 'artist', so probably should be used for an actor you respect, rather than those hardworking professionals who appear in daytime soap operas.
Solution 3:
I think you'd do better not to use it at all, for film actors or for any other kind. It has a jocular tone, and rather a feeble one at that, which you may wish to avoid.